TOKYO, Nov 2 (Reuters) - Advertising giant WPP said on Thursday it was taking legal action against partner Asatsu-DK Inc, deepening a row over the Japanese firm's backing for a $1.3 billion buyout offer from Bain Capital.

WPP, which holds 25 percent of Asatsu-DK, and other shareholders have said the bid by the U.S. private equity firm significantly undervalues the company.

Last month, Asatsu-DK said it had told WPP it planned to end their two-decade business alliance, and had asked WPP to sell its shares to Bain.

It said that, according to their contract, if WPP does not sell its shares to Asatsu-DK or a nominated party within a year of the Japanese firm's notification to terminate their alliance, WPP must sell its shares to the general public on the market.

The world's largest advertising agency responded in an emailed statement on Thursday that it was seeking arbitration with a Japanese arbitration body and a preliminary injunction with the Tokyo District Court.

In both cases, it is asking for a declaration that Asatsu-DK's planned termination of their business alliance was invalid, and Asatsu-DK had no right to request or require WPP to sell its shares.

A representative for Bain said the firm was confident the contract would stand up in court.

Bain has offered 3,660 yen per share in its tender offer, which opened on Oct. 3, and is seeking a stake of at least 50.1 percent.

David Gross-Loh, head of Bain's Asia business, told Reuters it would extend the tender offer deadline by about a week to Nov. 21 to give shareholders more time to consider the offer given WPP's legal action.

The extension is to comply with local financial requirements, he said, adding Bain's offer is full and final.

Shares in Asatsu-DK, which have traded above the offer level in the hope that Bain will raise its bid, closed down 0.4 percent on Thursday at 3,740 yen each.

Apart from WPP, London-based fund manager Silchester International and Hong Kong-based activist hedge fund Oasis Management Company have also said Bain's offer is too low.

Silchester owns 17 percent of Asatsu-DK and Oasis' holding is less than 5 percent.

Asatsu-DK and WPP formed their alliance in 1998 to set up joint ventures and cultivate clients together, and exchanged equity stakes, but the Japanese firm says that synergies from the tie-up failed to materialise.

Asatsu-DK said it has not received a notice about legal action from WPP, but is aware of the move through media reports. It declined to comment further.